arXiv subjects

Elizabeth Winstanley

Publications and source records attributed to Elizabeth Winstanley.

At least 55 records · Page 3Linked to original sources

arXiv2016

Stability of black holes in Einstein-charged scalar field theory in a cavity

Can a black hole that suffers a superradiant instability evolve towards a 'hairy' configuration which is stable? We address this question in the context of Einstein-charged scalar field theory. First, we describe a family of static black hole solutions which possess charged scalar-field hair confined within a mirror-like boundary. Next, we derive a set of equations which govern the linear, spherically symmetric perturbations of these hairy solutions. We present numerical evidence which suggests that, unlike the vacuum solutions, the (single-node) hairy solutions are stable under linear perturbations. Thus, it is plausible that stable hairy black holes represent the end-point of the superradiant instability of electrically-charged Reissner-Nordstrom black holes in a cavity; we outline ways to explore this hypothesis.

gr-qc↗

arXiv2016

On the stability of soliton and hairy black hole solutions of ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant

We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant $Λ$. These solutions are described by $N-1$ magnetic gauge field functions $ω_{j}$. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any $N$, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions $ω_{j}$ have no zeros, and satisfy a set of $N-1$ inequalities. In the gravitational sector, we are able to prove that there are solutions which have no instabilities in a neighbourhood of stable embedded ${\mathfrak {su}}(2)$ solutions, provided the magnitude of the cosmological constant $\left| Λ\right| $ is sufficiently large.

gr-qc↗

arXiv2016

On the stability of dyons and dyonic black holes in Einstein-Yang-Mills theory

We investigate the stability of four-dimensional dyonic soliton and black hole solutions of ${\mathfrak {su}}(2)$ Einstein-Yang-Mills theory in anti-de Sitter space. We prove that, in a neighbourhood of the embedded trivial (Schwarzschild-)anti-de Sitter solution, there exist non-trivial dyonic soliton and black hole solutions of the field equations which are stable under linear, spherically symmetric, perturbations of the metric and non-Abelian gauge field.

gr-qc↗

arXiv2016

Topological black holes in ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant

We investigate the phase space of topological black hole solutions of ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory in anti-de Sitter space with a purely magnetic gauge potential. The gauge field is described by $N-1$ magnetic gauge field functions $ω_{j}$, $j=1,\ldots , N-1$. For ${\mathfrak {su}}(2)$ gauge group, the function $ω_{1}$ has no zeros. This is no longer the case when we consider a larger gauge group. The phase space of topological black holes is considerably simpler than for the corresponding spherically symmetric black holes, but for $N>2$ and a flat event horizon, there exist solutions where at least one of the $ω_{j}$ functions has one or more zeros. For most of the solutions, all the $ω_{j}$ functions have no zeros, and at least some of these are linearly stable.

gr-qc↗

arXiv2015

Einstein-charged scalar field theory: black hole solutions and their stability

A complex scalar field on a charged black hole in a cavity is known to experience a superradiant instability. We investigate possible final states of this instability. We find hairy black hole solutions of a fully coupled system of Einstein gravity and a charged scalar field. The black holes are surrounded by a reflecting mirror. We also investigate the stability of these black holes.

gr-qc↗

arXiv2015

A menagerie of hairy black holes

According to the no-hair conjecture, equilibrium black holes are simple objects, completely determined by global charges which can be measured at infinity. This is the case in Einstein-Maxwell theory due to beautiful uniqueness theorems. However, the no-hair conjecture is not true in general, and there is now a plethora of matter models possessing hairy black hole solutions. In this note we focus on one such matter model: Einstein-Yang-Mills (EYM) theory, and restrict our attention to four-dimensional, static, non-rotating black holes for simplicity. We outline some of the menagerie of EYM solutions in both asymptotically flat and asymptotically anti-de Sitter space. We attempt to make sense of this black hole zoo in terms of Bizon's modified no-hair conjecture.

gr-qc↗

arXiv2015

Massless rotating fermions inside a cylinder

We study rotating thermal states of a massless quantum fermion field inside a cylinder in Minkowski space-time. Two possible boundary conditions for the fermion field on the cylinder are considered: the spectral and MIT bag boundary conditions. If the radius of the cylinder is sufficiently small, rotating thermal expectation values are finite everywhere inside the cylinder. We also study the Casimir divergences on the boundary. The rotating thermal expectation values and the Casimir divergences have different properties depending on the boundary conditions applied at the cylinder. This is due to the local nature of the MIT bag boundary condition, while the spectral boundary condition is nonlocal.

hep-th↗

arXiv2015

Vacuum polarization on the brane

We compute the renormalized expectation value of the square of a massless, conformally coupled, quantum scalar field on the brane of a higher-dimensional black hole. Working in the AADD brane-world scenario, the extra dimensions are flat and we assume that the compactification radius is large compared with the size of the black hole. The four-dimensional on-brane metric corresponds to a slice through a higher-dimensional Schwarzschild-Tangherlini black hole geometry and depends on the number of bulk space-time dimensions. The quantum scalar field is in a thermal state at the Hawking temperature. An exact, closed-form expression is derived for the renormalized expectation value of the square of the quantum scalar field on the event horizon of the black hole. Outside the event horizon, this renormalized expectation value is computed numerically. The answer depends on the number of bulk space-time dimensions, with a magnitude which increases rapidly as the number of bulk space-time dimensions increases.

gr-qc↗

arXiv2015

Renormalised fermion vacuum expectation values on anti-de Sitter space-time

The Schwinger-de Witt and Hadamard methods are used to obtain renormalised vacuum expectation values for the fermion condensate, charge current and stress-energy tensor of a quantum fermion field of arbitrary mass on four-dimensional anti-de Sitter space-time. The quantum field is in the global anti-de Sitter vacuum state. The results are compared with those obtained using the Pauli-Villars and zeta-function regularisation methods, respectively.

hep-th↗

arXiv2015

Hadamard renormalized scalar field theory on anti-de Sitter space-time

We consider a real massive free quantum scalar field with arbitrary curvature coupling on $n$-dimensional anti-de Sitter space-time. We use Hadamard renormalization to find the vacuum expectation values of the quadratic field fluctuations and the stress-energy tensor, presenting explicit results for $n=2$ to $n=11$ inclusive.

gr-qc↗

arXiv2014

The global rotating scalar field vacuum on anti-de Sitter space-time

We consider the definition of the global vacuum state of a quantum scalar field on $n$-dimensional anti-de Sitter space-time as seen by an observer rotating about the polar axis. Since positive (or negative) frequency scalar field modes must have positive (or negative) Klein-Gordon norm respectively, we find that the only sensible choice of positive frequency corresponds to positive frequency as seen by a static observer. This means that the global rotating vacuum is identical to the global nonrotating vacuum. For $n\ge 4$, if the angular velocity of the rotating observer is smaller than the inverse of the anti-de Sitter radius of curvature, then modes with positive Klein-Gordon norm also have positive frequency as seen by the rotating observer.We comment on the implications of this result for the construction of global rotating thermal states.

gr-qc↗

arXiv2014

Rotating quantum states

We revisit the definition of rotating thermal states for scalar and fermion fields in unbounded Minkowski space-time. For scalar fields such states are ill-defined everywhere, but for fermion fields an appropriate definition of the vacuum gives thermal states regular inside the speed-of-light surface. For a massless fermion field, we derive analytic expressions for the thermal expectation values of the fermion current and stress-energy tensor. These expressions may provide qualitative insights into the behaviour of thermal rotating states on more complex space-time geometries.

hep-th↗

arXiv2014

Dirac fermions on an anti-de Sitter background

Using an exact expression for the bi-spinor of parallel transport, we construct the Feynman propagator for Dirac fermions in the vacuum state on anti-de Sitter space-time. We compute the vacuum expectation value of the stress-energy tensor by removing coincidence-limit divergences using the Hadamard method. We then use the vacuum Feynman propagator to compute thermal expectation values at finite temperature. We end with a discussion of rigidly rotating thermal states.

gr-qc↗

arXiv2014

Hawking Radiation from Higher-Dimensional Black Holes

We review the quantum field theory description of Hawking radiation from evaporating black holes and summarize what is known about Hawking radiation from black holes in more than four space-time dimensions. In the context of the Large Extra Dimensions scenario, we present the theoretical formalism for all types of emitted fields and a selection of results on the radiation spectra. A detailed analysis of the Hawking fluxes in this case is essential for modelling the evaporation of higher-dimensional black holes at the LHC, whose creation is predicted by low-energy models of quantum gravity. We discuss the status of the quest for black-hole solutions in the context of the Randall-Sundrum brane-world model and, in the absence of an exact metric, we review what is known about Hawking radiation from such black holes.

hep-th↗

arXiv2013

Kermions

In the framework of quantum field theory in curved space-time, we study the quantization of a massless fermion field on a non-extremal Kerr black hole. The key theme in this note is the fundamental difference between scalar and fermion fields for the process of defining quantum states. In particular, we define two new states for fermions on Kerr which cannot be defined for quantum scalar fields on Kerr. These two states are the analogues of the standard Boulware and Hartle-Hawking states on a Schwarzschild black hole.

gr-qc↗

arXiv2013

Fermions on adS

We construct the Feynman propagator for Dirac fermions on anti-de Sitter space-time and present an analytic expression for the bi-spinor of parallel transport. We then renormalise the vacuum expectation value of the stress-energy tensor and end by analysing its renormalised expectation value at finite temperatures.

gr-qc↗

arXiv2013

Black holes, TeV-scale gravity and the LHC

Over the past 15 years models with large extra space-time dimensions have been extensively studied. We have learned from these models that the energy scale of quantum gravity may be many orders of magnitude smaller than the conventional value of 10^19 GeV. This raises the tantalizing prospect of probing quantum gravity effects at the LHC. Of the possible quantum gravity processes at the LHC, the formation and subsequent evaporation of microscopic black holes is one of the most spectacular. We give an overview of some of the fundamental ideas of the large extra dimensions scenarios and the resulting black hole processes at the LHC.

hep-th↗

arXiv2013

Kermions: quantization of fermions on Kerr space-time

We study a quantum fermion field on a background non-extremal Kerr black hole. We discuss the definition of the standard black hole quantum states (Boulware, Unruh and Hartle-Hawking), focussing particularly on the differences between fermionic and bosonic quantum field theory. Since all fermion modes (both particle and anti-particle) have positive norm, there is much greater flexibility in how quantum states are defined compared with the bosonic case. In particular, we are able to define a candidate `Boulware'-like state, empty at both past and future null infinity; and a candidate `Hartle-Hawking'-like equilibrium state, representing a thermal bath of fermions surrounding the black hole. Neither of these states have analogues for bosons on a non-extremal Kerr black hole and both have physically attractive regularity properties. We also define a number of other quantum states, numerically compute differences in expectation values of the fermion current and stress-energy tensor between two states, and discuss their physical properties.

gr-qc↗